The invention relates to a method for producing a composite plastic part (CK). A first fiber material (F1) is impregnated with a polyamide matrix polymer (PAM), thereby obtaining a matrix composition (MZ), onto which a surface composition (OZ) is applied, and a first plastic component (K1) is obtained. In a second step, a second plastic component (K2) is molded on the first plastic component (K1), whereby the composite plastic part (CK) is obtained. The invention further relates to the composite plastic part (CK) which can be obtained using the method according to the invention. The invention additionally relates to the use of polyethyleneimine (PEI) for improving the impregnation of the first fiber material (F1) with the polyamide matrix polymer (PAM).